Linear equations and functions By: Lindsay, Erin, Nora, Breigh, and Abbie Unit 2

2.1 Vocabulary Represent Relations and Functions Relation- a mapping or pairing of input values with output values. Domain- the set of input (x) values in a relation. Range- the set of output (y) values in a relation. Function- a relation for which each input has exactly one output. Equation in two variables- an equation that has an independent or input variable and a dependent or output variable that depends on the value of the input.

More 2.1 Vocabulary Linear Function- a function that can be written in the y=mx+b (slope-intercept) form. Where m and b are constants. Function Not A Function

Vertical Line Test A relation is a function if no vertical line intersects 2 points on the graph. Function Not a Function

Is the function linear? 1.f(x)=6x g(x)=2x²+4x-1

2.2 Find Slope and Rate of Change Slope-The slope m of a non vertical line is the ratio of the vertical change (the rise) to the horizontal change (the run) Parallel-Two lines in a plane that do not intersect Perpendicular-Two lines in a plane that intersect to form a right angle Rate of Change-How much one quantity changes, on average, relatives to the change in another quantity

Slope of a Line Algebra Graph

Classification of Lines by Slope Positive Slope rises from left to right Negative Slope falls from left to right Zero Slope is horizontal Undefined slope is vertical

Problems Find the slope of the line passing through the points (3,9) and (8,5) Without graphing tell whether the line the points (-7,3) and (3,2) rises, falls, is horizontal, or is vertical

Parallel and Perpendicular Lines Parallel Lines- Perpendicular Lines-

2.3 Graph Equations of Lines Parent Function-The most basic function in a family of functions Y-intercept-the y-coordinate of a point where the graph intersects the y-axis Slope-intersect form-An equation if the form y=mx+b with slope m and y-intercept b Standard form of a linear equation- the standard form of a linear equation Ax+By=C where A and B are not both 0 X-intercept- the coordinate of a point where a graph intersects the x-axis

Using Slope-Intercept Form Step 1- write the equation in slope-intercept form by solving for y. Step 2- Identify the y-intercept b and use it to plot the point (0,b) where the line crosses the y-axis Step 3- Identify the slope m and use it to plot a second point on the line. Step 4- Draw a line through the 2 points

Graph the equation using intercepts 2x+3y=12

Horizontal and Vertical Lines Horizontal Lines- The graph of y=c is the horizontal line through (0,C). Vertical Lines- The graph of x=c is the vertical line through (C,0).

2.4 Write Equations of Lines Write an equation of the line Through (1,5) with a slope of -2

More Problems 3. Through (-2,3) and (a) parallel and (b) perpendicular to y=4x-6 4.Through (6,2) and (3, -2)

2.8 Graph Linear Inequalities in Two Variables Linear Inequality in Two Variables- An inequality that can be written in one of the following forms: Solution of a Linear Inequality- An ordered pair (x,y) that makes the inequality true when the values x and y are substituted in the inequality Graph of a Linear Inequality-The set of points in a coordinate plane that represents the solutions of the inequality Half-plane- The two regions of a coordinate that are separated by6 the boundary line of a inequality

Problems Check whether is a solution of: 1. (5,2) 2.(-25,4)

Graphing a Linear Inequality Step 1- Graph the boundary line for the inequality. Use a dashed line for and a solid line for Step 2-Test a point not on the boundary line to determine whether it is a solution of the inequality. If it is a solution shade the half-plane containing the point. If it is not a solution, shade the other half-plane

Graph a Linear Inequality with One Variable Graph 3x-2y<-6 in a coordinate plane. Graph the boundary line 3x-2y=-6. Use a dashed line because the inequality symbol is <. Test the point (0,0). Because (0,0) is not a solution of the inequality, shade the half- plane that does not contain (0,0)